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Math Help - Complex Principal Argument #2

  1. #1
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    Complex Principal Argument #2

    (9+9i)^3
    I tried multipling out the number and then arctan( \frac{y}{x}) but its not right

    I also tried finding the \theta and dividing it by n, "3" ,but it is not the right answer.

    it turns out to be \frac{3\pi}{4}
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Fallen186 View Post
    (9+9i)^3
    I tried multipling out the number and then arctan( \frac{y}{x}) but its not right

    I also tried finding the \theta and dividing it by n, "3" ,but it is not the right answer.

    it turns out to be \frac{3\pi}{4}
    Note that 9+9i=9\left(1+i\right)=9e^{i\frac{\pi}{4}}.

    Thus, z=\left(9+9i\right)^3=9^3e^{i\frac{3\pi}{4}}\impli  es\text{Arg}\,z=\frac{3\pi}{4}

    Does this make sense?
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